On the classification of smooth Fano weighted complete intersections

Muhammad Imran Qureshi

doi:10.1007/s44426-025-00020-0

On the classification of smooth Fano weighted complete intersections

Muhammad Imran Qureshi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a complete classification of smooth Fano n-folds, 6≤n≤10, such that their images under their (sub)-anticanonical embedding can be described as a wellformed weighted complete intersection of some weighted projective space and they are not intersections with a linear cone. In total, we obtain 1180 families of such Fano manifolds by utilizing a combination of algorithmic and theoretical methods.

Original language	English
Article number	20
Journal	Acta Universitatis Sapientiae, Mathematica
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s44426-025-00020-0
State	Published - Dec 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Sapientia Hungarian University of Transylvania 2025.

Keywords

Complete intersection
Fano varieties
Weighted projective space

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s44426-025-00020-0

Cite this

@article{1bb50a97c4ea4db89dd84a1a41f6de71,

title = "On the classification of smooth Fano weighted complete intersections",

abstract = "We provide a complete classification of smooth Fano n-folds, 6≤n≤10, such that their images under their (sub)-anticanonical embedding can be described as a wellformed weighted complete intersection of some weighted projective space and they are not intersections with a linear cone. In total, we obtain 1180 families of such Fano manifolds by utilizing a combination of algorithmic and theoretical methods.",

keywords = "Complete intersection, Fano varieties, Weighted projective space",

author = "Qureshi, \{Muhammad Imran\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Sapientia Hungarian University of Transylvania 2025.",

year = "2025",

month = dec,

doi = "10.1007/s44426-025-00020-0",

language = "English",

volume = "17",

journal = "Acta Universitatis Sapientiae, Mathematica",

issn = "1844-6094",

publisher = "Springer International Publishing",

number = "1",

}

TY - JOUR

T1 - On the classification of smooth Fano weighted complete intersections

AU - Qureshi, Muhammad Imran

N1 - Publisher Copyright: © The Author(s), under exclusive license to Sapientia Hungarian University of Transylvania 2025.

PY - 2025/12

Y1 - 2025/12

N2 - We provide a complete classification of smooth Fano n-folds, 6≤n≤10, such that their images under their (sub)-anticanonical embedding can be described as a wellformed weighted complete intersection of some weighted projective space and they are not intersections with a linear cone. In total, we obtain 1180 families of such Fano manifolds by utilizing a combination of algorithmic and theoretical methods.

AB - We provide a complete classification of smooth Fano n-folds, 6≤n≤10, such that their images under their (sub)-anticanonical embedding can be described as a wellformed weighted complete intersection of some weighted projective space and they are not intersections with a linear cone. In total, we obtain 1180 families of such Fano manifolds by utilizing a combination of algorithmic and theoretical methods.

KW - Complete intersection

KW - Fano varieties

KW - Weighted projective space

UR - https://www.scopus.com/pages/publications/105021541765

U2 - 10.1007/s44426-025-00020-0

DO - 10.1007/s44426-025-00020-0

M3 - Article

AN - SCOPUS:105021541765

SN - 1844-6094

VL - 17

JO - Acta Universitatis Sapientiae, Mathematica

JF - Acta Universitatis Sapientiae, Mathematica

IS - 1

M1 - 20

ER -

On the classification of smooth Fano weighted complete intersections

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this